Find $\lim _ { x \rightarrow 9 ^ { - } } \frac { x - 9 } { x ^ { 2 } - 81 }$.

Name: Find $\lim _ { x \rightarrow 9 ^ { - } } \frac { x - 9 } { x ^ { 2 } - 81 }$.
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Question

Quizplus · Accepted Answer

The given limit can be simplified by factoring the denominator as $\lim _ { x \rightarrow 9 ^ { - } } \frac { x - 9 } { (x + 9)(x - 9) }$, which simplifies to $\lim _ { x \rightarrow 9 ^ { - } } \frac { 1 } { x + 9 }$. Substituting $x = 9$, we get $\frac { 1 } { 18 }$.

Find lim⁡x→9−x−9x2−81\lim _ { x \rightarrow 9 ^ { - } } \frac { x - 9 } { x ^ { 2 } - 81 }limx→9−​x2−81x−9​

Find $\lim _ { x \rightarrow 9 ^ { - } } \frac { x - 9 } { x ^ { 2 } - 81 }$